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<h1>Design of Tangent Vector Fields</h1>
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<span>
<a href="http://graphics.stanford.edu/~mdfisher/publications.html">Matthew Fisher</a>
<sup>1</sup>
</span>
<span>
<a href="http://www.multires.caltech.edu/pubs/pubs.htm">Peter Schröder</a>
<sup>2</sup>
</span>
<span>
<a href="http://www.geometry.caltech.edu/~mathieu/">Mathieu Desbrun</a>
<sup>2</sup>
</span>
<span>
<a href="http://research.microsoft.com/en-us/um/people/hoppe/">Hugues Hoppe</a>
<sup>3</sup>
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<div id="affiliationsD">
<span>
<sup>1</sup>
Stanford University
</span>
<span>
<sup>2</sup>
California Institute of Technology
</span>
<span>
<sup>3</sup>
Microsoft Research
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<img id="teaserD" src="papers/vectorFieldDesignTeaser.png"/>
<span>ACM Transactions on Graphics (Proc. SIGGRAPH 2007)</span>
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<h2>Abstract</h2>
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<p>
Tangent vector fields are an essential ingredient in controlling surface appearance for applications ranging from anisotropic shading to texture synthesis and non-photorealistic rendering. To achieve a desired effect one is typically interested in smoothly varying fields that satisfy a sparse set of user-provided constraints. Using tools from Discrete Exterior Calculus, we present a simple and efficient algorithm for designing such fields over arbitrary triangle meshes. By representing the field as scalars over mesh edges (i.e., discrete 1-forms), we obtain an intrinsic, coordinate-free formulation in which field smoothness is enforced through discrete Laplace operators. Unlike previous methods, such a formulation leads to a linear system whose sparsity permits efficient pre-factorization. Constraints are incorporated through weighted least squares and can be updated rapidly enough to enable interactive design, as we demonstrate in the context of anisotropic texture synthesis.
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<h2>Extras</h2>
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Paper: <a href="papers/vectorFieldDesign.pdf"><img src="Images/pdf-icon.png"/>PDF</a>
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Google Scholar: <a href="http://scholar.google.com/citations?view_op=view_citation&hl=en&user=PUSWc4EAAAAJ&citation_for_view=PUSWc4EAAAAJ:u5HHmVD_uO8C"><img src="Images/google-icon.png"/></a>
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BibTeX citation:
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@inproceedings{fisher2007design,
<br/>
  title={Design of tangent vector fields},
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  author={Fisher, Matthew and Schr{\"o}der, Peter and Desbrun, Mathieu and Hoppe, Hugues},
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  booktitle={ACM Transactions on Graphics (TOG)},
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  volume={26},
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  number={3},
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  pages={56},
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  year={2007},
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  organization={ACM}
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}
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